Yes, calculations can be used in your surveys. This is done in a similar way to the calculations used in study forms. The survey calculations can only refer to variables within the survey, and therefore survey calculations cannot reference study or report variables.
If you don't want the respondents to see the results, you can set the calculations to be hidden. The output of the hidden calculations will be included in the export of your survey data.
You can also use the record metadata, such as the record ID and the institute in your surveys, if necessary.